If I have a partial derivative for $A_\mu$ of the form $$\frac{\partial A_\mu}{\partial(\partial_\mu A_\upsilon)}$$ where $\partial_\mu A_\upsilon = \frac{\partial A_\upsilon}{\partial x^\mu}$ is the derivative of $A_\upsilon$ with respect to the spacetime coordinates, how do I go about evaluating this expression? In Sean Carroll's Intro to GR, he gets terms like these in equations that he seems to just discard, so I suspect the answer is $0$, but I don't know the specifics of how that results from the derivative above.
Asked
Active
Viewed 25 times
0
-
Which eq? Which page? – Qmechanic Jun 17 '23 at 21:35
-
1Possible duplicates: https://physics.stackexchange.com/q/885/2451 , https://physics.stackexchange.com/q/526011/2451 and links therein. – Qmechanic Jun 17 '23 at 22:01
-
@Qmechanic It would take a while to put in the equation. Should I edit the question? – Chidi Jun 17 '23 at 22:03
-
Also, the first duplicate you provided answered my question. The equation was indeed the Lagrangian for electromagnetism in flat spacetime, and I did not know that the arguments of the Lagrangian were considered independent of each other. – Chidi Jun 17 '23 at 22:07